Introduction Background Examples Example 1 Problems Run Simulation References Credits Assessment Etomica Modules

We can treat adsorption from a mixture of gases (at low pressures) by extending the Langmuir isotherm:

${\displaystyle A(g)+S\rightleftharpoons A(ads)}$

${\displaystyle B(g)+S\rightleftharpoons B(ads)}$

These reactions are not independent because both species compete for the same surface sites. The two equilibria must be solved simultaneously:

${\displaystyle {\frac {[A(ads)]}{P_{A}\times [S]}}=K_{A}}$

${\displaystyle {\frac {[B(ads)]}{P_{B}\times [S]}}=K_{B}}$

As for the one-component case, we define surface coverages ${\displaystyle \theta _{A}=[A(ads)]/[S]_{0}}$ and ${\displaystyle \theta _{B}=[B(ads)]/[S]_{0}}$, and note that

${\displaystyle [S]+[A(ads)]+[B(ads)]=[S]_{0}}$, or ${\displaystyle [S]/[S]_{0}=1-\theta _{A}-\theta _{B}}$

Then,

${\displaystyle K_{A}={\frac {\theta _{A}}{P_{A}\times (1-\theta _{A}-\theta _{B})}}}$

${\displaystyle K_{B}={\frac {\theta _{B}}{P_{B}\times (1-\theta _{A}-\theta _{B})}}}$

and dividing, we get

${\displaystyle {\frac {\theta _{A}}{\theta _{B}}}={\frac {P_{A}}{P_{B}}}{\frac {K_{A}}{K_{B}}}}$

The ratio of A:B on the surface is therefore different than the ratio of A:B in the gas phase, by precisely ${\displaystyle {K_{A}}/{K_{B}}}$, so the more strongly adsorbed component is enriched on the surface. This is referred to as the thermodynamic selectivity, the preference of the surface for one species of a mixture, and is the basis for many techniques to separate gas mixtures.